GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 25 Aug 2019, 21:53

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# How many factors of the number 2^3 x 3 x 5^2 are perfect squares?

Author Message
TAGS:

### Hide Tags

e-GMAT Representative
Joined: 04 Jan 2015
Posts: 3018
How many factors of the number 2^3 x 3 x 5^2 are perfect squares?  [#permalink]

### Show Tags

Updated on: 13 Aug 2018, 02:08
1
5
00:00

Difficulty:

85% (hard)

Question Stats:

32% (01:00) correct 68% (00:57) wrong based on 185 sessions

### HideShow timer Statistics

Originally posted by EgmatQuantExpert on 27 Feb 2018, 09:40.
Last edited by EgmatQuantExpert on 13 Aug 2018, 02:08, edited 4 times in total.
Senior Manager
Joined: 13 Oct 2016
Posts: 251
GMAT 1: 600 Q44 V28
Re: How many factors of the number 2^3 x 3 x 5^2 are perfect squares?  [#permalink]

### Show Tags

27 Feb 2018, 09:56
1
1
The answer should be 4 as per the logic explained in the below link by various moderators:

https://gmatclub.com/forum/how-many-factors-of-10800-are-perfect-squares-251823.html
_________________
_______________________________________________
If you appreciate the post then please click +1Kudos
e-GMAT Representative
Joined: 04 Jan 2015
Posts: 3018
Re: How many factors of the number 2^3 x 3 x 5^2 are perfect squares?  [#permalink]

### Show Tags

27 Feb 2018, 22:36
2
1

Solution

• Per our conceptual knowledge, a number is a perfect square only when the exponents of the prime factors in the number are even.
o For example: $$7^2$$is a perfect square but $$5^3$$ is not, since the exponent of $$7$$is even but the exponent of $$5$$is not.
• To find the factors which are perfect squares we need to first of focus on each prime number and its powers and try to find out, what are the possible perfect squares that we can create using those prime numbers.
• So, for making perfect squares, we need even powers of the prime factors and this can be written in the form: $$2^a * 3^b * 5^c$$ [where a, b and c can be 0,2,4,8…]
o The factors of$$2^3$$ are: $$1, 2, 4, 8$$ out of which only $$1(2^0)$$ and $$4(2^2)$$ are perfect squares.
o The factors of $$3$$ are: $$1$$ and $$3$$, out of which only $$1(3^0)$$ is a perfect square.
o The factors of $$5^2$$are: $$1, 5, 25,$$ out of which only $$1(5^0)$$ and $$25(5^2)$$ are perfect squares.
• Thus, the possible unique perfect square factors using only these prime numbers are $$1$$, $$4$$ and $$25$$.
But is that all?
Look at the following factor:
• Is $$2^2$$ *$$5^2$$ a perfect square?
o Yes, it is.
So, the criterion of perfect squares also holds true when we multiply 2 or more such perfect squares together.
o Hence, 100 will also be included in our list.
So, there are 4 possible cases where the factors of the given number are perfect squares.
Hence, the correct answer is Option D.
_________________
Director
Joined: 19 Oct 2018
Posts: 791
Location: India
Re: How many factors of the number 2^3 x 3 x 5^2 are perfect squares?  [#permalink]

### Show Tags

06 May 2019, 09:42
Any factor of 2^3∗3∗5^2 can be written as 2^a* 3^b* 5^c
For factor to be a perfect square-
a can have 2 values (0,2)
b can have 1 value (0)
c can have 2 values (0,2)
Total factors of the number 2^3∗3∗5^2 are perfect squares= 2*1*2=4
Re: How many factors of the number 2^3 x 3 x 5^2 are perfect squares?   [#permalink] 06 May 2019, 09:42
Display posts from previous: Sort by